The trial in the second-degree murder case for his fatal shooting of Florida teen Trayvon Martin remains set for June 10

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George Zimmerman watches during his hearing at the Seminole County Courthouse on October 19, 2012 in Sanford, Florida.

A judge in the case of a former neighborhood watch leader accused of shooting Florida teenager Trayvon Martin denied a request by defense attorneys to delay the trial Tuesday.

George Zimmerman's attorneys presented a motion Tuesday asking Judge Debra Nelson to push the trial from mid-June back to November because they say the prosecutor has been slow to turn over needed evidence. The state attorney has denied the accusation.

Nelson denied the motion and said the trial will begin on June 10. She noted that Zimmerman's lead attorney has been on the case for nearly a year and a half and said the problems he's having getting evidence are not insurmountable.

Zimmerman's attorney, Mark O'Mara, said he wants to try the case in June but also wants to do it the right way.

"I will call my wife as an expert witness that I want this case tried in June," O'Mara said Tuesday. "There is no benefit to the defense team, there is certainly no benefit to Mr. Zimmerman and there is no benefit to the Martin family to keep this case going. I am very sensitive to that, but the reality is we have to try it once.

Prosecutor Bernie de la Rionda argued that the amount of preparation for the case is the result of Zimmerman's attorneys.

"I have never had a case, at least here in central Florida, as a normal thing where the defense creates their own website, creates their own Facebook , creates their own Twitter and just publishes stuff out there, encourages discussion among various groups," de la Rionda said. "I find it ironic that the defense complains they are now having to address all these issues, that with all due respect to the defense, they helped create."

Zimmerman is claiming he acted in self-defense in shooting Martin last year and has pleaded not guilty to second-degree murder.

Tuesday also happens to be what would have been Martin's 18th birthday, and his parents plan to celebrate the occasion with events throughout the week.

Community leaders and college students said a prayer and sang "Happy Birthday" before Tuesday's hearing in Sanford, and community leaders will be holding a "Banding Together for Peace" event later in the day.

On Saturday, Martin's parents will hold a "Peace Walk" at 10 a.m. at Ives Estate Park in Miami. On Sunday, they will hold a "remembrance Dinner" at 5 p.m. at the DoubleTree Miami Airport Hotel.

All of the proceeds for the event will go to the Trayvon Martin Foundation.